@stdlib/stats
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Standard library statistical functions.
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{{alias}}( t, α, β )
Evaluates the moment-generating function (MGF) for a gamma distribution with
shape parameter `α` and rate parameter `β` at a value `t`.
If `α <= 0` or `β <= 0`, the function returns `NaN`.
If `α` or `β` is `NaN`, the function returns `NaN`.
Parameters
----------
t: number
Input value.
α: number
Shape parameter.
β: number
Rate parameter.
Returns
-------
out: number
Evaluated MGF.
Examples
--------
> var y = {{alias}}( 0.5, 0.5, 1.0 )
~1.414
> y = {{alias}}( 0.1, 1.0, 1.0 )
~1.111
> y = {{alias}}( -1.0, 4.0, 2.0 )
~0.198
> y = {{alias}}( NaN, 1.0, 1.0 )
NaN
> y = {{alias}}( 0.0, NaN, 1.0 )
NaN
> y = {{alias}}( 0.0, 1.0, NaN )
NaN
> y = {{alias}}( 2.0, 4.0, 1.0 )
NaN
> y = {{alias}}( 2.0, -0.5, 1.0 )
NaN
> y = {{alias}}( 2.0, 1.0, 0.0 )
NaN
> y = {{alias}}( 2.0, 1.0, -1.0 )
NaN
{{alias}}.factory( α, β )
Returns a function for evaluating the moment-generating function (MGF) of a
gamma distribution with shape parameter `α` and rate parameter `β`.
Parameters
----------
α: number
Shape parameter.
β: number
Rate parameter.
Returns
-------
mgf: Function
Moment-generating function (MGF).
Examples
--------
> var myMGF = {{alias}}.factory( 3.0, 1.5 );
> var y = myMGF( 1.0 )
~27.0
> y = myMGF( 0.5 )
~3.375
See Also
--------